“This would be a bold acquisition to make,” said Frederick Ilchman, the chair of European paintings at the Museum of Fine Arts, Boston. He and his team of curators were gazing, fascinated, at a 16th-century portrait of Antonietta Gonzales, a girl with hypertrichosis, a rare congenital condition that causes excessive facial hair growth. The elegantly dressed young lady holds an inscription stating that she is the daughter of Don Pietro, a “wild man” from the Canary Islands who lived in the court of the Duke of Parma.

This extraordinary, long-lost portrait by Lavinia Fontana was an outstanding example of the many works by women artists on show Thursday at the bustling preview of the TEFAF Maastricht fair in the Netherlands. (The event opens to the public Saturday and runs through March 14.) The Fontana portrait was priced at 4.5 million euros, about $5 million, on the booth of the Geneva-based dealership Rob Smeets. Across the aisle, Artemisia Gentileschi’s recently rediscovered “Penitent Magdalene,” from about 1626, was available on the booth of the dealers Robilant and Voena at $7 million.

Ilchman has regularly traveled from Boston to TEFAF since 2007; in that time, the focus of his acquisitions has evolved. “Last year we bought five paintings in one day: three of them were by women. This has been a priority in the last few years,” Ilchman said. “We do not have a lot of work by women painters or decorative artists. It seems like a useful task to amend this discrepancy,” he added, acknowledging that museums with large holdings of pre-20th-century art can seem disconnected from the 21st century’s cultural concerns.

Museums are increasingly important buyers at TEFAF Maastricht, as the number of private individuals purchasing old master pictures, sculptures and antiques has declined. Collecting tastes have changed in the digital age, and the vast majority of new art buyers are drawn to contemporary works. The acquisition funds of many institutions, particularly in the United States, encourage purchases that maintain the encyclopedic nature of museum collections. At the same time, curators are looking for old art that can resonate with a new audience.

The delegation from Boston — which also included Matthew Teitelbaum, the museum’s director, and the board of trustees president Marc Plonskier — was one of some 20 groups of curators and patrons from well-funded American institutions at the first preview day of TEFAF Maastricht, according to Magda Grigorian, the fair’s head of communications. Grigorian added that around 300 museum directors would be among the event’s 50,000 expected visitors.

“The fair has become more difficult. It isn’t like 10 or 15 years ago,” said the Geneva-based old master specialist​​ Salomon Lilian, one of some 270 dealers exhibiting this year. “The museums compensate for the decline of private buying,” he added. “A1 quality paintings are still very much in demand; small Dutch cabinet paintings are much more difficult.”

TEFAF Maastricht has tried to keep up with the times. This year, galleries specializing in modern and contemporary art outnumbered dealers in more traditional pictures by 55 to 52. While few contemporary collectors regard it as a must-attend event, the fair now has a credible roster of contemporary galleries, including White Cube, Galeria Continua, Mennour and Sean Kelly.

“We know the collectors at contemporary art fairs. Here we meet different clients,” said Kelly, whose gallery is based in New York and Los Angeles, and who was showing at TEFAF Maastricht for a second time.

Kelly was one of the few contemporary dealers to embrace the historical diversity of TEFAF Maastricht — works from his stable of artists were hung next to complementary older objects — and he also offered a desirable work by an in-demand artist of the moment: Kehinde Wiley’s imposing 2020 “Portrait of Issa Diatta,” priced at $650,000.

Discovering, discussing and pricing museum-quality works from the last 7,000 years — and sometimes even buying them on the spot — remains the primary mission for the curators at TEFAF Maastricht. During the first hours of the preview, the Virginia Museum of Fine Arts acquired a touching terra cotta portrait of a boy by the French Napoleonic-period sculptor Joseph Chinard, priced at $90,000 on the booth of the London-based sculpture specialist Stuart Lochhead. Lochhead said an American museum, which he declined to name, had also purchased a late 16th-century Giambologna bronze of the striding war god Mars, with an asking price of $4 million.

Gerhard Lutz, a medievalist in a group of half a dozen curators visiting from the Cleveland Museum, was impressed by a small stone statue of the prophet Isaiah attributed to the 14th-century Flemish sculptor Claus Sluter, priced at €500,000 on the booth of the London dealer Sam Fogg. Lutz’s Ohio-based museum contains three characterful weeping alabaster statues by Sluter’s pupil, Claus de Werve. “Works like this can shed light on things that we own,” Lutz said.

Curators were also drawn to the hauntingly minimal 1641 canvas, “A Pear and Apples on a Pewter Plate,” by the Spanish still life painter Juan de Zurbarán, priced at $2.8 million with the New York dealer Nicholas Hall. Others marveled at a rare group of paintings by Nazarene artists — 19th-century Germany’s precursors to the English Pre-Raphaelites — on the booth of the Texas-based Gallery 19C.

“You don’t get the historical depth or the quality at any other fair,” said Eric Lee, the director of the Kimbell Art Museum in Fort Worth.

But what did he think of the increasing number of contemporary dealers showing at the fair? “It’s a great idea. It brings in new collectors who might get interested in older art,” Lee said. “You can buy a major old master painting for the price of a third-tier Andy Warhol.”

Trying to convince today’s art fairgoers that older works are good value for money is the key challenge for the organizers and exhibitors at TEFAF Maastricht. For the museum curators who continue to buy old works, it’s convincing the public that such art is relevant.